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...ls emitted by the two processes. Example 11.1. We return to Example 2.1, which is concerned with a pedestrian who uses a crossing with traffic lights to cross a road with busy traffic safely. In 8 In =-=[11, 9]-=-, this process is rather contradictory called the non-existent process. Its new name was prompted by the fact that after performing an action no process will ever proceed as this process. 27sExample 9...

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...,r} ∧ d• = 0) ⊓� c1(��appr) · ∂H(T near � Cdn � Gop ))) X2 = ∂H(T near � C dn � G op ) Let φ2 denote proposition (−1000 ≤ x ≤ 0 ∧ 40 ≤ ˙x ≤ 52 ∧ d ≤ 5 ∧ ˙ d = 1 ∧ r = 90 ∧ ˙r = 0). X2 = φ2 ∩� V ( � s∈=-=[0,5]-=- σs rel ((d• = 0 ∧ r • = • r ∧ C {x}) ⊓� c2(lower) �� · ∂H(T near � Cidle � Gdn ))) X3 = ∂H(T near � C idle � G dn ) Let φ3 denote proposition (−1000 ≤ x ≤ 0 ∧ 40 ≤ ˙x ≤ 52 ∧ ˙ d = 0 ∧ r ≥ 0 ∧ ˙r = −2...

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...g. [35] for a comparison of the continuous and stochastic approaches. There are a variety of computational approaches to hybrid modelling, such as hybrid I/O automata [36] and hybrid process algebras =-=[37]-=-. We plan to build on this tradition and extend cπ with discrete features, in the form of species present as single individuals. Interactions with these species will act as discrete control events on ...

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...epressilator [9], in which genes can be switched on or off by interactions with their environment (more precisely, with transcription factor proteins). The behaviour of such systems can be regarded as a collection of sets of ODEs, the discrete events shifting the dynamic behaviour from the control of one set of ODEs to another. This is the approach taken with hybrid automata [13]. Process algebras have the advantage of being compositional hence models are built out of subcomponents and we aim to fully exploit this feature in HYPE. Existing process algebras for hybrid systems include ACP srths [3], hybrid χ [22], φ-calculus [20] and HyPA [6]. In [16], Khadim shows substantial differences in the approaches taken by these process algebras relating to syntax, semantics, discontinuous behaviour, flow-determinism, theoretical results and availability of tools. However, they are all similar in their approach in that the dynamic behaviour of each subcomponent must be fully described with the ODEs for the subcomponent given explicitly in the syntax of the process algebra, before the model can be constructed. We aim for a finer-grained approach where each subcomponent is built up from a number ...

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...ysis of the behaviour of various systems. Serious efforts have been made in the past to deal with various systems (e.g. discrete event systems [20,25], real-time systems [10,12,26] and hybrid systems =-=[1, 3, 5, 6, 17, 27]-=-) in a process algebraic way. Over the years, process algebras have been successfully used in a wide range of problems and in practical applications in both academia and industry for analysis of many ...

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...putational systems are described in an algebraic way, and analyzed using symbolic manipulation. Very recently, process algebras have been developed in which hybrid systems can be modeled and analyzed =-=[17, 9, 6, 23]-=-. In this report, we give a short presentation of such a hybrid process algebra, called HyPA [9], and then focus on the analysis of safety for actions and safety for predicates of hybrid processes in ...